Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension

TL;DR

This paper investigates how topological order in a quantum loop gas model is affected by magnetic perturbations, revealing a quantum phase transition driven by vortex condensation that impacts quantum computation.

Contribution

It demonstrates the stability of topological order under small loop tension and characterizes the quantum phase transition caused by increasing tension in a toric code model.

Findings

Topological order persists at low loop tension.

A continuous quantum phase transition occurs at critical tension.

Topological order breaks down when coupled to an Ohmic heat bath.

Abstract

We study the stability of topological order against local perturbations by considering the effect of a magnetic field on a spin model -- the toric code -- which is in a topological phase. The model can be mapped onto a quantum loop gas where the perturbation introduces a bare loop tension. When the loop tension is small, the topological order survives. When it is large, it drives a continuous quantum phase transition into a magnetic state. The transition can be understood as the condensation of `magnetic' vortices, leading to confinement of the elementary `charge' excitations. We also show how the topological order breaks down when the system is coupled to an Ohmic heat bath and discuss our results in the context of quantum computation applications.